❓ What is Shear Resistance of Concrete Section (VRd,c) in Eurocode 2?

Shear resistance of a concrete section, VRd,c in Eurocode 2(BSEN1992-1-1:2004), is the design shear capacity provided by the concrete itself without shear reinforcement. In simple terms, VRd,c tells us how much shear force a concrete member can resist before shear links are required.

In short, the formula for VRd,c is:

Design Value of Shear Resistance of Concrete Section
Eq 6.2(a), BSEN 1992-1-1:2004

🤔 Why Do We Need to Know (VRd,c)

VRd,c is used to check whether the applied design shear force VEd can be resisted by the concrete section alone.

If VEd ≤ VRd,c :

then minimum or no shear reinforcement may be required, depending on the member type and Eurocode 2 detailing rules.

If VEd > VRd,c :

then shear reinforcement must be provided .

🧩 Dependance of VRd,c

From Eurocode 2, VRd,c mainly depends on: Cl. 6.2.2, BSEN 1992-1-1:2004

Width, bw Depth, d Concrete Strength, fck Do we need shear links? Section

  • Concrete strength, fck

  • Longitudinal reinforcement ratio, ρl

  • Effective depth, d and depth ratio, k

  • Section width, bw

  • Axial stress, σcp

🧩 Details of Formula of VRd,c

The formula of VRd,c is an empirical formula, not a first-principles derivation. It is based on test results and calibrated design rules, rather than direct force equilibrium alone.Eq. 6.2a, BSEN 1992-1-1:2004:

Design Value of Shear Resistance of Concrete Section
Eq 6.2(a), BSEN 1992-1-1:2004
where
fck in MPa
k = 1 +
ρl =
Asl = area of tensile reinforcement
bw = smallest width of corss-section in tensile area
σcp =
NEd = axial force
Ac= area of concrete cross section
CRd,c= 0.18/γc
k1= 0.15


Also the VRd,c need to be larger than below formula Eq. 6.2b, BSEN 1992-1-1:2004:

minimum of VRd,c
Eq 6.2(b), BSEN 1992-1-1:2004
where
vmin= 0.035 k3/2fck1/2

🧮 Quick Calculator for VRd,c for rectangular beam section

Use the calculator below to quickly estimate VRd,c based on the Eurocode 2 formula.

Eurocode 2 concrete shear resistance calculator

VRd,c
—
Concrete shear resistance
Section properties
mm
mm
MPa
-
MPa
usually 0.18/γc
-

Minimum Shear Reinforcement Requirement

For beam sections, minimum shear reinforcement is still required according to Clause 6.2.1(4), BSEN 1992-1-1:2004, even when VEd ≤ VRd,c.

The minimum shear reinforcement ratio is given by: Eq. 9.5N, BSEN 1992-1-1:2004

min of shear reinforcement ratio
- This is a detailing requirement to ensure minimum shear capacity and ductility.
- Only slab sections may omit minimum shear reinforcement where transverse redistribution of loads is possible.

📄 Need a Full Design Check Report?

The calculator above is intended for quick estimation only. For actual design work, use our full to run the complete Eurocode 2 shear check and generate a ready-to-submit PDF report.

📝Summary & Key Takeaways

  1. Shear resistance of a concrete section, VRd,c in Eurocode 2, is the design shear capacity provided by the concrete itself without shear reinforcement.
  2. VRd,c is determined by Eq. 6.2a, BSEN 1992-1-1:2004 with minimum value Eq. 6.2b, BSEN 1992-1-1:2004.
  3. If the section is beam, even design action VEd smaller than shear resistance of concrete section VRd,c, minimum shear reinforcement need to be provided due to detailing requirement.
  4. The minimum shear reinforcement for detailing requirement is Eq. 9.5N, BSEN 1992-1-1:2004.
#rc design #shear design #glossary #structural
CivilSimple Team

CivilSimple Team

The CivilSimple Team writes practical engineering guides for the profession and the curious. All articles are reviewed for technical accuracy before publication.